WASHINGTON — U.S. Sen. Angus King joined lawmakers from both parties Wednesday in announcing a proposal to prevent a doubling of the interest rate on certain federal student loans, an increase that would affect 7 million college students in the coming school year.

On Monday, the rate on subsidized Stafford loans will rise to 6.8 percent from 3.4 percent unless Congress intervenes. The loans, targeting undergraduate students in financial need, do not accrue interest while the students are in school.

In a press release Wednesday, King said he was “pleased to join this bipartisan group of Senators in putting forward a sensible, compromise proposal that will not only lower student loan interest rates for millions of students, but will also maintain important protections and adopt a market-based approach to get Congress out of the business of setting arbitrary rates with no connection to the actual cost of borrowing.”

“Our solution successfully builds on the many credible proposals put forward by members on both sides of the aisle, as well as the President,” King said, “to help make college an affordable reality. This bipartisan bill demonstrates that we can bridge the partisan divide and work together in the best interest of the American people.”

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It is unclear whether lawmakers will be able to get a bill to President Obama before the deadline. The Republican-led House in May passed a bill that would tie interest rates on federal education loans to the government’s cost of borrowing, with the interest on each individual loan varying from year to year. The Democratic-led Senate so far has deadlocked over the issue, failing to pass Republican or Democratic proposals. Many congressional Democrats want a two-year extension of the 3.4 percent rate, which Republicans say would be too costly.

On Wednesday, Sens. Joe Manchin III (D-W.Va.), Lamar Alexander (R-Tenn.), Richard Burr (R-N.C.), Tom Coburn (R-Okla.) and Angus King (I-Maine) announced a plan that they said would yield lower rates for students and parents and bring more certainty for borrowers, while saving the government $1 billion over 10 years. King, an independent, caucuses with Democrats.

Under their plan, the rate for undergraduate Stafford loans — regardless of whether they are subsidized — would be set each year at the yield on the 10-year Treasury bill plus 1.85 percentage points, according to a statement Manchin released. This year, that would translate to an effective interest rate of less than 4 percent.

Certain other federal loans, for graduate students and parents, also would be tied to the yield on the 10-year T-bill plus a higher markup.

The interest rate for each loan would be fixed after the money is borrowed. The senators said students worried about excessive interest rates, should the government’s cost of borrowing rise, would have the option of consolidating their federal loans at a rate no higher than 8.25 percent.

“This bipartisan agreement not only makes sure student rates will not double on July 1, but this is a long-term fix that will lower rates for all students and will save students $30 billion over the next three years, making sure anyone who wants an education, can afford one,” Manchin said in his statement.

Hurdles were immediately apparent.

Adam Jentleson, a spokesman for Senate Majority Leader Harry M. Reid (D-Nev.), said late Wednesday: “There is no deal on student loans that can pass the Senate because Republicans continue to insist that we reduce the deficit on the backs of students and middle-class families, instead of closing tax loopholes for the wealthiest Americans and big corporations.”

Sen. Tom Harkin (D-Iowa), chairman of the Health, Education, Labor and Pensions Committee, wants a firm cap on interest rates, said his spokeswoman Allison Preiss. “Any proposal that lacks a cap is a nonstarter,” she said.